The lord chancellor has warned ministers that exempting MPs from freedom of information inquiries will damage public confidence in the principles of open government.

A leaked letter from Lord Falconer, seen by the Guardian, shows that the cabinet is split on whether to back a private member's bill to exempt parliament and MPs' correspondence from the Freedom of Information Act. Jack Straw, Margaret Beckett and Peter Hain want to back the bill so it can be debated by parliament.

Mr Straw's support is crucial because he can control the parliamentary timetable as the leader of the house, which could give the bill a fair wind. Opponents include Hilary Armstong, the Cabinet Office minister, Lord Rooker, an environment department minister, and Gerry Sutcliffe, a junior Home Office minister.

The letter shows that ministers were so at odds with each other that they decided to keep quiet when the bill was up for debate by parliament earlier this month.

Lord Falconer expresses concern that the measure would add to the perception "of being an increasingly secretive government" because he is already consulting on measures to curb the use of the act by journalists and the public. These include limiting media and other organisations to four inquiries a year and increasing the scope for ministers to reject applications on the grounds of cost.

The bill has been tabled by the Conservative party's former chief whip, David Maclean. He wants to exempt parliament and MPs' letters from the act because he says new government guidance to 100,000 public authorities on releasing MPs' letters is complex and unclear. It would also exempt the Commons and the Lords from the act, limiting wider disclosure of MPs' expenses and allowances.

The bill passed a second reading without debate during a crowded parliamentary agenda on the day Westminster was convulsed by the dawn arrest of Ruth Turner, a Downing Street aide, over the "cash for honours" inquiry.

The letter reveals that Mr Maclean has the support of Mr Straw. It quotes him as saying that "many members on both sides of the house would welcome it, not because they opposed the general operation of the Freedom of Information Act, but because of the special circumstances of parliament". Mr Hain, the Northern Ireland secretary, thought the bill should be fully debated even though present legislation should be wide enough to protect MPs.

Lord Falconer discloses that he will hold a ministerial meeting to discuss whether to back or block the act.

Maurice Frankel, director of the Campaign for Freedom of Information, said: "If parliament is to have any credibility, it cannot push through constitutional legislation through a private member's bill without, so far, any discussion."